[R-sig-Geo] Two scale process in experimental variogram - how to fit a theoretical variogram?

[Tom Gottfried]

Hi,

Am 14.10.2011 13:29, schrieb philsen:
> Hi Tom,
>
> thanks for the answer, but I am explicit interested in the direction
> perpendicular to the row, due to imaging direction of the radar
> satellite. In addition, we also acquired DSMs in parallel to the rows,
> which as you mentioned do not show these behaviour. However, an
> anisotropic variogram perpendicular to the rows shows the same variogram
> as the attached omnidirectional.

... because the shape of your investigation area imposes anisotropy to any semivariance with lag > 
100 m.

Let me comment on your interpretation of the maxima in your variogram: You have minima at multiples 
of 150 m, corresponding to the spacing between tractor tracks (seems to be a small tractor?). The 
narrow "valleys" surrounding these minima indicate strong similarity between the tractor tracks and 
higher variability between them. A short scale periodicity of seedbed rows does not seem to be visible.
Back to your original question: I can't think of something that fits better than an exponential or 
spherical plus a periodical model. Though this does not represent the narrow valleys very well as 
the periodical model is basically a sine.

regards,
Tom

>
> cheers,
>
> Philip
>
> -------- Original-Nachricht --------
> Betreff: 	Re: [R-sig-Geo] Two scale process in experimental variogram -
> how to fit a theoretical variogram?
> Datum: 	Fri, 14 Oct 2011 12:50:19 +0200
> Von: 	Tom Gottfried<tom.gottfried at tum.de>
> An: 	r-sig-geo at r-project.org
>
>
>
> Hi Philip,
>
> though this does not answer your question: tractor tracks and seedbed rows suggest strong anisotropy
> and a periodical structure perpendicular to them. If you are interested in roughness induced by
> different tillage practices (i.e. seedbed preparation) you might be more interested in only the
> anisotropic variogram parallel to tracks and rows, thus excluding the effects of wheels and seeding
> machinery.
>
> HTH anyhow,
> Tom
>
> Am 14.10.2011 12:19, schrieb philsen:
>>   Dear list,
>>
>>   I am trying to characterize different tillage patterns of agricultural
>>   fields using variogram analysis for microwave remote sensing. Basis for
>>   the analysis is a high resolution DSM with a 2x2  mm^2 resolution and a
>>   size of 1x6 m^2 (see pdf at
>>   URL:http://www.geographie.uni-muenchen.de/department/admin/lehre/upload/1094/Disp_Vario_Surface.pdf).
>>
>>   The aim is to characterize the horizontal roughness component by using
>>   the autocorrelation length /l/ derived from an autocorrelation function
>>   (ACF) at which e.g. the exponential ACF drops under 1/e.
>>
>>   When using a subsample of 10000 points the variogram is calculated using
>>   gstat by
>>
>>     >library(gstat)
>>     >data<-
>>   read.table(url("http://www.geographie.uni-muenchen.de/department/admin/lehre/upload/1094/subsample_DSM.csv"),
>>   header=TRUE)
>>     >maxdist=max(dist(data, method="maximum"))/2
>>     >coordinates(data)<- c("X","Y")
>>     >v<- variogram(Z~1, data, cutoff=maxdist, width=5)
>>     >plot(v)
>>
>>      From my understanding, there are two processes of different scale
>>   visible. The first maximum of the experimental variogram is related to
>>   the small scale seedbed rows, while the second max. is related to the
>>   appearance of tractor tracks with a distance of ca. 150 cm (see DGM-plot
>>   in pdf).
>>
>>   So the question is how to fit a theoretical variogram to the data, which
>>   allows me to characterize both processes in terms of an autocorrelation
>>   length /l/_1 and /l/_2?
>>
>>      From searching trough the archive I have found a discussion about
>>   nested variograms. Therefore I tried to fit the sum of two exponential
>>   variogram models to my data:
>>
>>     >nest.vfit<- fit.variogram(v, model=vgm(1, "Exp", 90, add.to=vgm(1,
>>   "Exp", 200)))
>>     >plot(v, nest.vfit)
>>
>>   However I am not sure about the output? To characterize /l/_1 and /l/_2,
>>   I think I need at least two theoretical variograms to invert
>>   /C(h) = 1 - ?(h) / ?(inf)/ with /C/(h)= fitted ACF at distance h
>>
>>   Hopefully there is somebody who can help me .....
>>
>>   Kind regards,
>>
>>   Philip
>>
>
>
>
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email: tom.gottfried at wzw.tum.de
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